There are several types of fur. Bears and Wolves have furs that are specific to them, i.e. Bear Fur and Wolf Fur. Deer and undomesticated Mouflon drop a generic fur. (Mouflon which have turned into Sheep after domestication drop Sheepskin.) Furs have three sizes, small, medium, and large.
Cut fur into clothing pieces by right-clicking the ground while holding fur or fur scrap in your hand while you have a knife in your inventory. When a large fur is cut for clothing pieces, it returns a medium fur scrap and a small fur scrap. When a medium fur scrap is cut, it returns a small fur scrap. This means a large fur or large fur scrap can be cut into four clothing pieces.
Animal Head Hat
Wolves and bears have a 50% chance to drop a complete fur when killed instead of a fur scrap. This fur can be crafted with a knife in the crafting grid to produce a fur head hat and a fur scrap. The fur scrap can be used for fur clothing crafting methods. If you only have a generic fur or fur scrap, you can still craft a generic fur hat using regular clothing sewing.
Generic furs and fur scraps can also be crafted with a knife in the crafting grid to get a rawhide of the same size.
Additionally, furs and fur scraps can be used to construct a Teepee.